Monday, January 09, 2012
... /////

This paper by a former student of Richard Lindzen finally managed to fix Milutin Milankovič's theory which hadn't worked and the outcome was a theory that does work. The graph below contains both theoretical predictions as well as the observed data about the Northern Hemisphere temperature and you may see that the match is beautiful:

As the TRF article mentioned above shows, previous attempts to make the theory work displayed the right frequencies but the graphs never really agreed. The probability that the agreement above is coincidental is pretty much zero. Lots of high-frequency wiggles agree. In the future, one may optimize the Milankovič theory but these will be incremental improvements; the qualitative fact that the astronomical cycles dictate "most" of the dynamics in the glaciation cycles has been established by the graphs above.

The key correction that Roe had to add was a "derivative" that was previously neglected. So the two quantities that he may successfully compare are:

the time derivative of the observed ice volume in the last 750,000 years or so (white)

the calculated Arctic Circle insolation in June (cyan)

The time derivative used to be neglected in the past; people tried to link the insolation directly to the amount of ice. But what the Sun near the Arctic circle is doing is not to determine the volume of ice from scratch; instead; the amount of solar radiation decides about the melting or growth of the ice, i.e. about its derivative.

In the following year, I contacted Gerard Roe and he sent me the detailed data that were used to draw all his graphs etc.: a perfectly transparent scientific approach. However, it was still largely useless for my goal – to calculate the future ice ages – because much of the data was taken from tables published in other papers. They only published the insolation in the past; they didn't provide us with the algorithms to calculate the cycles (such as the precession etc.) which means that I couldn't calculate the future evolution, either.

So even though we know the detailed dynamics and maths that produces the spectacular agreement depicted by the picture above, I am not sure whether there is a paper that carefully applies Roe's method to predict the future. Let me know if you know about such a paper, I am extremely interested in it. Just to be sure: I am not interested in Milankovič-like papers that ignore Roe's critical findings. In the last 5 years, all such quantitative papers should be considered rubbish and I surely do consider them rubbish because the error that Roe fixed was really critical.

CO2 and next ice age

Now, in the last 24 hours, BBC, The Telegraph, and many others wrote about a new paper by Luke Skinner et al. in Nature Geosciences. The paper says that CO2 will save us from the coming new ice age which is great.

It's refreshing to see that CO2 is sometimes getting good press. You really don't want the temperatures to drop by 10 °C. On the other hand, all the other "details" that are being written about these questions are preposterous beyond imagination.

It's being said that the warm era between two ice ages is usually around 11,000 years (whatever is the exact definition of the boundaries) but we have already enjoyed over 11,500 years since the last ice age so a new ice age is overdue. Well, those things are not periodic so it is nonsensical to expect that it's always the same 11,000 years. And I still don't have the full Milankovič-Roe projection of the future ice ages so I can't say whether the expectation is right. If they only use some analogy with the moment 780,000 years ago but ignore Roe's model, then I will consider the claim untrustworthy.

Dynamics of CO2 concentration after fossil fuels

However, what's even more absurd is the role that is being attributed to CO2. CO2 will only be modified due to the human activity for a few centuries which is much shorter than the time needed for the ice age cycles to collect several Celsius degrees – that requires thousands or tens of thousands of years.

In particular, we will probably run out of fossil fuels in less than 300 years. I am being generous here; my expectation would be lower. At the peak, there will be some concentration which may be anywhere between 600 and 2000 ppm. I don't know how far the mankind will get. I am just sure that once the concentration will reach 1000 ppm, people will already be realizing very well that there's nothing wrong about such elevated concentrations and they will be able to understand that 2000 ppm isn't a problem, either.

If the civilization happens to abandon fossil fuels extremely quickly, for whatever reasons, like in 80 years from now (no, sorry, I surely don't think that you will live when fossil fuels become mostly irrelevant!), the peak concentration may be just 600 ppm or so; today, it's about 392 ppm.

But what I want to discuss again is what the CO2 concentration will do afterwards. If we stopped producing CO2 tonight, the CO2 concentration would decrease by 2 ppm a year, at least for a couple of initial years before it gets much lower. Why? It's easy to see why. We may calculate that if all the CO2 we emit stayed in the air, the concentration would increase by 4 ppm a year. But because it only grows by 1.9 ppm or so, about 2.1 ppm of CO2 must be absorbed every year by "stimulated sinks".

It's clear that this absorption by 2.1 ppm is stimulated by the "already elevated concentration of CO2" itself, not by the annual production during the last year. The oceans and the plants don't care whether a CO2 molecule was emitted during the last year or not. They can't even "measure" the answer to this question. They are absorbing and consuming CO2 because there is already an excess CO2 in the air – above the equilibrium concentration which would be about 280 ppm for the current temperature – and they simply don't care whether the CO2 concentration keeps on rising or not. What matters for the amount of sinks is the excess concentration, not its time derivative!

So out of those 390 ppm we have today, the sinks would subtract 2 ppm a year which is about 2% of the excess, 390-280 ppm, of the CO2. So at least initially, the sinks liquidate 2% of the excess CO2 above the equilibrium level every year. It takes 50 years for the excess to drop 2.718 times or so. I hope that you understand exponentially decreasing functions.

The oceans and the biosphere are attracting the CO2 concentration towards the equilibrium value which is 280 ppm for the temperature today. However, if there will be a coming ice age, the equilibrium CO2 concentration will be lower. After all, we know that it was around 180 ppm in the coldest parts of the ice ages.

So if the astronomical cycles were suddenly changed in 2012 so that we should have an ice age which is almost 10 °C cooler and whose equilibrium CO2 concentration is 180 ppm, the excess CO2 – the difference of 390 ppm and 180 ppm – would be about 200 ppm, about twice as large. This would also mean that all the sinks' activity is doubled. It would follow that every year, they would absorb 4 ppm, everything we emit: the CO2 concentrations would stop rising despite our continuing business-as-usual production of CO2!

Alternatively, you may think about the year 2500. Imagine that people are able to keep the CO2 concentration high by 2500 – which is something they will surely want (because it increases the efficiency of agriculture by dozens of percent) but it may be hard. However, they will no longer be able to make substantial CO2 emissions. So the excess of CO2 above the equilibrium concentration will be dropping by those 2 percent a year. If we are entering an ice age, the temperature will be lower and so will be the equilibrium CO2 concentration. Consequently, the excess CO2 will be even bigger and the sinks will operate more vigorously.

At any rate, it's nonsensical to imagine that the CO2 will change the geological history at the timescale of ice ages. Those take thousands of years to change the temperature by a degree. However, in a thousand of years, both the CO2 concentration and the temperature that could have been sightly modified by the elevation of CO2 concentrations will return so close to the "natural" values that no one will be able to tell the difference.

Some of the media write that it will take "thousands of years" for the excess CO2 to be absorbed. But we know that this is just invalid. The calculation using the status quo shows that the excess drops 2.718 times every 50 years. But we also possess the observed historical data that unequivocally refute the claim that it takes thousands of years for the temperature to return: it's the famous CO2-temperature correlation shown by Al Gore.

The correct interpretation of the correlation is that the oceans and the biosphere are able to store an amount of CO2 and other gases that depends on their temperatures: for example, warmer oceans tend to release the gases to the atmosphere, thus increasing the atmospheric concentration.

And the CO2-temperature correlation is very good and the synchronization works pretty well. In average, the gases move 600 years after the temperature. So in average, it took 600 years for the oceans and the biosphere to adjust the CO2 to the equilibrium level. This is really an overestimate of the time after which "most of the excess or deficit CO2" is extracted or returned to the atmosphere. A better definition of these questions and more accurate models would be needed to yield more accurate numbers.

(I suspect that the ability of oceans to emit or absorb goes down when they mostly slow down or freeze; that's why the "motion back towards the equilibrium concentration" may get slower, comparable to 600 years, when the temperatures are low. The figure "50 years" for the reduction of the excess by a factor of 2.718 may only be reasonable for thriving warm eras such as the current one.)

Quite generally, it's nonsensical to imagine that the CO2-caused greenhouse effect may matter during most of a glaciation cycle. It just can't. This fact is directly seen in the Vostok ice core data because the changes of the CO2 are lagging behind the changes of the temperature. This shows that the influence of the temperature on the concentration has always been more important than the opposite influence.

We may estimate that it was about 20 times more important. Why? It's simple. Let's calculate the coefficient linking the changes of CO2 and changes of temperature.

In an official document of a ministry-of-education program, I was also mentioned as a fan of Ewa Farna so I feel I am obliged to occasionally embed her song (Polish song, in this case, see Czech edition) that I listened to many times today. ;-)

In Nature, the warming by almost 10 °C, from an ace age to an interglacial, was needed to raise the CO2 concentration from 180 ppm to 280 ppm. So you have 10 °C per 100 ppm. On the other hand, we have also added 100 ppm of CO2 which strengthened the greenhouse effect. But we know that the resulting warming was comparable to 0.5 °C (and maybe less than that!) which is 20 times smaller than those 10 °C that this paragraph started with. So in this symmetric treatment of the two effects, the CO2 greenhouse effect is 20 times weaker than the opposite influence of the temperature on the CO2 concentration via outgassing of the oceans and changes in the biosphere.

Twenty is a pretty high number. The fact that twenty is much greater than one is the reason why one may neglect the CO2 greenhouse effect in all discussions of the glaciation cycles. And vice versa: we may neglect the glaciation cycles which are too slow in the rest of the "fossil fuel era" which will only last for 500 years including the subsequent drop of CO2 in the atmosphere. So even though you may be happy that CO2 is sometimes being attributed a positive role, the role of the "savior who will save us from the next ice age", the underlying logic is still the same pseudoscience. Those people still attribute CO2 some amazing importance for the climate which it doesn't have and which it has never had. It's sad to see that most of the science journalists and probably also climatologists (and related geologists) are incompetent but it's probably inevitable.

snail feedback (12)
:

Dear Harlow, methane is irrelevant for the climate, indeed. In the newest, unusually candid article at RealClimate.ORG, it was explained that even if the release of methane by the Arctic jumped 100 times relatively to how fast it is today, the temperature effect of methane would still be just the same as what the effect of CO2 is - with the extra vice that methane is absorbed much earlier than CO2.

Forget about methane. It's a few times more potent than CO2 per unit volume but the amount of methane that is being added to the atmosphere is totally negligible.

The flatness of the Vostok core data in the current peak is intriguing when compared with the previous peaks, a lot more acute. Moreover, it seems that this cup or flatness starts about the time that humans go from hunter-gatherers to crop farming and animal husbandry.

I believe that it is insolation that sets the general condition but that it is the various solar maxima and minima that provide the perturbation that "kick" the system from one state to the other and that it is Arctic Sea ice cover that determines the hysteresis that keeps us in one state or the other.

If we are in a glacial state, we remain there until we get a solar maximum that warms the Earth at the same time that summer NH insolation is high and allows the Arctic Sea ice to melt (even though the surrounding landmass might still have very thick ice). If insolation is not enough, we simply have an interstadial event and return to glacial conditions.

If we are in an interglacial, once NH insolation decays enough and we get a solar minimum, the Arctic Ocean freezes (and the ocean cools) enough that after we come out of the minimum we don't have enough energy to melt to Arctic Ocean ice cap and the increase in albedo keeps us in the glacial state until the cycle repeats.

So ... insolation sets the condition for which way the system is "leaning" but solar activities (possibly moderated or amplified by volcanic activity) are the "kick" which move us from one stable state to the other. The Arctic Ocean ice being the determining factor.

Dear Crosspatch, if we're in a "glacial state", how do you call the state we were in during the ice age? ;-)

Alejandro, not sure whether you interpret the plateau right. There's much more time resolution so the graph is thicker in the y-direction in the recent years, and gets smoother as you go into the past. Some diffusion, probably. So you may hide many things into the thick band. But there's not much evidence that it's been flatter in recent millenniums.

Just to be sure, "flat climate" is the optimum that the AGW warriors want to achieve, so if your argument were right, the humans actually manage to bring the Earth closer to the perfect flat Earth shape that the AGW jihadists fight for.

Dear Carl, as I said, papers such as this Imbrie squared are just pure rubbish. Just look at the graphs of the past temperatures to see that they don't agree. Just compare the degree of agreement in their paper with the agreement from the Roe paper included in my blog entry.

They don't use the valid theory so it can't be trusted when extrapolated to the future, either.

The paper was written in 1980, about 25 years before Roe, so it can't be right.

Quite generally, you don't seem to have any quality filters whatsoever.

Andre Berger is your man for modeling celestial mechanics related to Milankovitch cycles. He is an astronomer and is thesis is that the present interglacial will be similar to the MIS 11 which occurred 400,000 years ago and lasted 50,000 years. During that interglacial sea level rose about 20 meters or so. In many places worldwide we can see elevated terraces from that period when a lot of ice melted.

So take your pick. Get buried in ice when the glaciers form or move to higher ground when they melt.

Me, I prefer to keep warm and don't mind hilly land. If more CO2 will do it, bring on the CO2.